If vectors $\mid v\text{⃗}\mid =12$, $|u ⃗ |=100$ and the angle between $v\text{⃗}$ & $u ⃗$ is $\(\theta\)=\(\frac{\pi}{6}\)$, calculate $v ⃗⋅u ⃗$ .

If vectors $v\text{⃗}=⟨4,3⟩$ and $u\text{⃗}=⟨9,1⟩$, calculate $v\text{⃗}\cdot u\text{⃗}$.

If vectors $v\text{⃗}=12\hat{ı}$ and $u\text{⃗}=100\hat{ȷ}$, calculate $u\text{⃗}\cdot v\text{⃗}$.

If vectors $a\text{⃗}=13\hat{ı}$, $\text{⃗}b\text{⃗}=5\hat{ı}-12\hat{ȷ}$, and $c\text{⃗}=24\hat{ȷ}$, calculate $b\text{⃗}\cdot (a\text{⃗}-c\text{⃗})$.

If vectors $\mid a\text{⃗}\mid =3$ and $\mid b\text{⃗}\mid =7$, and $a\text{⃗}\cdot b\text{⃗}=14.85$, determine the angle between vectors $a\text{⃗}$ and $b\text{⃗}$.

If vectors $a\text{⃗}=4\hat{ı}$ and $b\text{⃗}=3\hat{ı}-2\hat{ȷ}$, determine the angle between vectors $a\text{⃗}$ and $b\text{⃗}$.